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# If a and b are integers, and m=a+b, is m divisible by 9?

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If a and b are integers, and m=a+b, is m divisible by 9?  [#permalink]

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21 Sep 2016, 03:52
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64% (01:29) correct 36% (01:40) wrong based on 110 sessions

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If a and b are integers, and m=a+b, is m divisible by 9?

(1) a is divisible by 9

(2) b=9a+4

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Re: If a and b are integers, and m=a+b, is m divisible by 9?  [#permalink]

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21 Sep 2016, 04:21
Bunuel wrote:
If a and b are integers, and m=a+b, is m divisible by 9?

(1) a is divisible by 9

(2) b=9a+4

Stat 1: We don't know have information about b...Insufficient.

Stat 2: b = 9a+4

if a = 1 then b = 13 , then m = 14 not divisible by 9

if a = 5 , b = 49 then m = 54 divisible by 9...insufficient.

Both : a is divisible by 9 , then let's take 81+4 = 85

m = 9+85 = 84..not divisible by 9.

IMO option C.
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Re: If a and b are integers, and m=a+b, is m divisible by 9?  [#permalink]

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21 Sep 2016, 05:22
A) a is divisible by 9 but there is no information about b b could be 1,2,3 etc in that case m=a+b will not be divisible by 9, not suff

B) b=9a+4 this tells that b is not divisible of 9 but no information on a, so not suff

A and B together, a is divisible by 9 whereas b =9a+4 let a=9 and b = 9*9+4 = 85 , so a+b not divisible by 9.
If we bifurcate m/9 = a/9 + 9a/9 + 4/9 , 4/9 will never be divisible by 9

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Re: If a and b are integers, and m=a+b, is m divisible by 9?  [#permalink]

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21 Sep 2016, 07:33
(1) a is divisible by 9

m = a + b = 9+1 = 10 -- not divisible by 9
m = a + b = 9+9 = 18 -- Divisible by 9

-- Not sufficient.

(2) b=9a+4

m = a + 9a + 4 = 10a+4 ==> 10+4 = 14 -- Not divisible by 9
m = a + 9a + 4 = 10a+4 ==> 50+4 = 54 -- Divisible by 9

-- Not sufficient.

$$m/9 = 10 * \frac{a}{9} + 4/9$$

If we combine (1) and (2), 4/9 will always be remainder of $$\frac{m}{9}$$. So, m is not divisible by 9.

Ans. C
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Re: If a and b are integers, and m=a+b, is m divisible by 9?  [#permalink]

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01 Jan 2019, 19:30
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Re: If a and b are integers, and m=a+b, is m divisible by 9?   [#permalink] 01 Jan 2019, 19:30
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